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A sender wants to persuade multiple homogeneous receivers to vote in favor of a proposal. Before the vote sender commits to a signal which sends private, potentially correlated, messages to receivers that are contingent on the true state of the world. The best equilibrium for sender in the resulting incomplete information game is unappealing: all receivers vote in favor of sender's preferred outcome, irrespective of their message. We therefore focus on the equilibrium where receivers vote sincerely, that is they vote in favor of the outcome that is optimal given their posterior. We characterize the optimal public and the optimal private signal, both for the case where receivers are behavioral and vote sincerely as well as the case where such behavior is a Bayes–Nash equilibrium (BNE). For the optimal public signal, sincere voting is a BNE, but the optimal private signal is subject to the swing voter's curse. Imposing the constraint that sincere voting be a BNE leads to an optimal signal where receivers are never pivotal. [ABSTRACT FROM AUTHOR]

We study bankruptcy problems in financial networks in the presence of general bankruptcy laws. The set of clearing payment matrices is shown to be a lattice, which guarantees the existence of a greatest clearing payment and a least clearing payment. Multiplicity of clearing payment matrices is both a theoretical and a practical concern. We present a new condition for uniqueness that generalizes all the existing conditions proposed in the literature. Our condition depends on the decomposition of the financial network into strongly connected components. A strongly connected component that contains more than one agent is called a cycle, and the involved agents are called cyclical agents. If there is a cycle without successors, then one of the agents in such a cycle should have a strictly positive endowment. The division rule used by a cyclical agent with a strictly positive endowment should be positive monotonic, and the rule used by a cyclical agent with a zero endowment should be strictly monotonic. Because division rules involving priorities are not positive monotonic, uniqueness of the clearing payment matrix is a much bigger concern for such division rules than for proportional ones. As a final contribution of the paper, we exhibit the relationship between the uniqueness of clearing payment matrices and the continuity of bankruptcy rules, a property that is very much desired for stability of financial systems. Funding: This research was supported by the Higher Education Institutional Excellence Program 2020 of the Ministry of Innovation and Technology in the framework of the "Financial and Public Services" research project [Grant TKP2020-IKA-02] at Corvinus University of Budapest. P. Csóka received funding from the National Research, Development and Innovation Office [Grants K-120035 and K-138826]. [ABSTRACT FROM AUTHOR]

We consider a situation in which agents have mutual claims on each other, summarized in a liability matrix. Agents' assets might be insufficient to satisfy their liabilities, leading to defaults. In case of default, bankruptcy rules are used to specify the way agents are going to be rationed. A clearing payment matrix is a payment matrix consistent with the prevailing bankruptcy rules that satisfies limited liability and priority of creditors. Since clearing payment matrices and the corresponding values of equity are not uniquely determined, we provide bounds on the possible levels equity can take. Unlike the existing literature, which studies centralized clearing procedures, we introduce a large class of decentralized clearing processes. We show the convergence of any such process in finitely many iterations to the least clearing payment matrix. When the unit of account is sufficiently small, all decentralized clearing processes lead essentially to the same value of equity as a centralized clearing procedure. As a policy implication, it is not necessary to collect and process all the sensitive data of all the agents simultaneously and run a centralized clearing procedure. History: Accepted by Yinyu Ye, optimization. Funding: P. Csoka was supported by the Hungarian National Research, Development, and Innovation Office [PD 105859], the Hungarian Academy of Sciences [LP-004/2010], and COST Action IC1205 on Computational Social Choice. Keywords: networks * bankruptcy problems * systemic risk * decentralized clearing * indivisibilities * blockchain, 1. Introduction The treatment of bankruptcy of countries, banks, firms, organizations, and individuals will always be a challenge for society. In the original bankruptcy problem, starting with the seminal paper [...]